The use of nonorthogonal functions to support single-particle states is ubiquitous in contemporary density functional theory, indeed, it is practically obligatory if one wishes to construct a method for which the effort scales with system size. As a result, it is of increasing importance to understand the measures which must be taken to accommodate it. In this talk I will begin by going “back to basics”, exploring the consequences of support function nonorthogonality and attempting to shed light on the accompanying notation and terminology so often used by linear-scaling DFT practitioners.

For many tasks we may wish to change the support functions during the course of a calculation. For example, in ONETEP a set of nonorthogonal generalised Wannier functions (NGWFs) are optimised to accurately minimise the total energy, in DFT +U the nonorthogonal Hubbard projectors may be made consistent with the NGW Fs (projector self-consistency) or optimised to meet another criterion such as providing a maximal the U tensor, and in linear-scaling TDDFT one may wish to propagate the support functions in time in order to achieve plane-wave accuracy. I will analyse the consequences of support function optimisation in each of these cases on geometric grounds and, on that basis, demonstrate a first-principles method to improve both the numerical stability and speed of such calculations.